4.2 Exercises
From Förberedande kurs i matematik 1
m (Robot: Automated text replacement (-Svar +Answer)) |
m (Robot: Automated text replacement (-{{:4.2 - Figur - Rätvinklig triangel med vinkeln v och sidor 3 och 5}} +{{:4.2 - Figure - A right-angled triangle with angle v and sides 3 and 5}})) |
||
(21 intermediate revisions not shown.) | |||
Line 2: | Line 2: | ||
{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | {| border="0" cellspacing="0" cellpadding="0" height="30" width="100%" | ||
| style="border-bottom:1px solid #000" width="5px" | | | style="border-bottom:1px solid #000" width="5px" | | ||
- | {{ | + | {{Not selected tab|[[4.2 Trigonometric functions|Theory]]}} |
- | {{ | + | {{Selected tab|[[4.2 Exercises|Exercises]]}} |
| style="border-bottom:1px solid #000" width="100%"| | | style="border-bottom:1px solid #000" width="100%"| | ||
|} | |} | ||
Line 13: | Line 13: | ||
|a) | |a) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle 27° and sides x and 13}} |
|b) | |b) | ||
|width="50%" | | |width="50%" | | ||
- | {{:4.2 - | + | {{:4.2 - Figure - A right-angled triangle with angle 32° and sides x and 25}} |
|- | |- | ||
|c) | |c) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle 40° and sides 14 and x}} |
|d) | |d) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle 20° and sides 16 and x}} |
|- | |- | ||
|e) | |e) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle 35° and sides 11 and x}} |
|f) | |f) | ||
|width="50%" | | |width="50%" | | ||
- | {{:4.2 - | + | {{:4.2 - Figure - A right-angled triangle with angle 50° and sides x and 19}} |
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:1|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:1|Solution a |Solution 4.2:1a|Solution b |Solution 4.2:1b|Solution c |Solution 4.2:1c|Solution d |Solution 4.2:1d|Solution e |Solution 4.2:1e|Solution f |Solution 4.2:1f}} |
===Exercise 4.2:2=== | ===Exercise 4.2:2=== | ||
Line 37: | Line 37: | ||
|a) | |a) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle v and sides 2 and 5}} |
|b) | |b) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle v and sides 70 and 110}} |
|- | |- | ||
|c) | |c) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle v and sides 5 and 7}} |
|d) | |d) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angle v and sides 3 and 5}} |
|- | |- | ||
|e) | |e) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - A right-angled triangle with angles v and 60° and side 5}} |
|f) | |f) | ||
- | |width="50%" | {{:4.2 - | + | |width="50%" | {{:4.2 - Figure - An isosceles triangle with top angle v and sides 2, 3 and 3}} |
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:2|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:2|Solution a |Solution 4.2:2a|Solution b |Solution 4.2:2b|Solution c |Solution 4.2:2c|Solution d |Solution 4.2:2d|Solution e |Solution 4.2:2e|Solution f |Solution 4.2:2f}} |
===Exercise 4.2:3=== | ===Exercise 4.2:3=== | ||
Line 71: | Line 71: | ||
|width="33%" | <math>\cos{\left(-\displaystyle \frac{\pi}{6}\right)}</math> | |width="33%" | <math>\cos{\left(-\displaystyle \frac{\pi}{6}\right)}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:3|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:3|Solution a |Solution 4.2:3a|Solution b |Solution 4.2:3b|Solution c |Solution 4.2:3c|Solution d |Solution 4.2:3d|Solution e |Solution 4.2:3e|Solution f |Solution 4.2:3f}} |
===Exercise 4.2:4=== | ===Exercise 4.2:4=== | ||
Line 91: | Line 91: | ||
|width="33%" | <math>\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}</math> | |width="33%" | <math>\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:4|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:4|Solution a |Solution 4.2:4a|Solution b |Solution 4.2:4b|Solution c |Solution 4.2:4c|Solution d |Solution 4.2:4d|Solution e |Solution 4.2:4e|Solution f |Solution 4.2:4f}} |
===Exercise 4.2:5=== | ===Exercise 4.2:5=== | ||
Line 106: | Line 106: | ||
|width="25%" | <math>\tan{495^\circ}</math> | |width="25%" | <math>\tan{495^\circ}</math> | ||
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:5|Solution a | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:5|Solution a |Solution 4.2:5a|Solution b |Solution 4.2:5b|Solution c |Solution 4.2:5c|Solution d |Solution 4.2:5d}} |
===Exercise 4.2:6=== | ===Exercise 4.2:6=== | ||
Line 113: | Line 113: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
| | | | ||
- | |width="100%" | <center> {{:4.2 - | + | |width="100%" | <center> {{:4.2 - Figure - Two triangles with angles 45° and 60°, respectively, and height difference x}} </center> |
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:6|Solution | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:6|Solution |Solution 4.2:6}} |
===Exercise 4.2:7=== | ===Exercise 4.2:7=== | ||
Line 122: | Line 122: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
| | | | ||
- | |width="100%" | <center> {{:4.2 - | + | |width="100%" | <center> {{:4.2 - Figure - A river}} </center> |
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:7|Solution | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:7|Solution |Solution 4.2:7}} |
===Exercise 4.2:8=== | ===Exercise 4.2:8=== | ||
Line 132: | Line 132: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
| | | | ||
- | |width="100%" | <center> {{:4.2 - | + | |width="100%" | <center> {{:4.2 - Figure - Hanging rod}} </center> |
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:8|Solution | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:8|Solution |Solution 4.2:8}} |
===Exercise 4.2:9=== | ===Exercise 4.2:9=== | ||
Line 141: | Line 141: | ||
{| width="100%" cellspacing="10px" | {| width="100%" cellspacing="10px" | ||
| | | | ||
- | |width="100%" | <center> {{:4.2 - | + | |width="100%" | <center> {{:4.2 - Figure - A road from A to B via P and Q}} </center> |
|} | |} | ||
- | </div>{{#NAVCONTENT:Answer|Answer 4.2:9|Solution | | + | </div>{{#NAVCONTENT:Answer|Answer 4.2:9|Solution |Solution 4.2:9}} |
Current revision
Theory | Exercises |
Exercise 4.2:1
Using the trigonometric functions, determine the length of the side marked\displaystyle \,x\,
a) |
| b) |
|
c) |
| d) |
|
e) |
| f) |
|
Exercise 4.2:2
Determine a trigonometric equation that is satisfied by \displaystyle \,v\,.
a) |
| b) |
|
c) |
| d) |
|
e) |
| f) |
|
Exercise 4.2:3
Determine
a) | \displaystyle \sin{\left(-\displaystyle \frac{\pi}{2}\right)} | b) | \displaystyle \cos{2\pi} | c) | \displaystyle \sin{9\pi} |
d) | \displaystyle \cos{\displaystyle \frac{7\pi}{2}} | e) | \displaystyle \sin{\displaystyle \frac{3\pi}{4}} | f) | \displaystyle \cos{\left(-\displaystyle \frac{\pi}{6}\right)} |
Exercise 4.2:4
Determine
a) | \displaystyle \cos{\displaystyle \frac{11\pi}{6}} | b) | \displaystyle \cos{\displaystyle \frac{11\pi}{3}} | c) | \displaystyle \tan{\displaystyle \frac{3\pi}{4}} |
d) | \displaystyle \tan{\pi} | e) | \displaystyle \tan{\displaystyle \frac{7\pi}{6}} | f) | \displaystyle \tan{\left(-\displaystyle \frac{5\pi}{3}\right)} |
Exercise 4.2:5
Determine
a) | \displaystyle \cos{135^\circ} | b) | \displaystyle \tan{225^\circ} | c) | \displaystyle \cos{330^\circ} | d) | \displaystyle \tan{495^\circ} |
Exercise 4.2:6
Determine the length of the side marked \displaystyle \,x\,.
|
Exercise 4.2:7
In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct?
|
Exercise 4.2:8
A rod of length \displaystyle \,\ell\, hangs from two ropes of length \displaystyle \,a\, and \displaystyle \,b\, as shown in the figure. The ropes make angles \displaystyle \,\alpha\, and \displaystyle \,\beta\, with the vertical. Determine a trigonometric equation for the angle \displaystyle \,\gamma\, which the rod makes with the vertical.
|
Exercise 4.2:9
The road from A to B consists of three straight parts AP, PQ and QB, which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at P and Q in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from A to B. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.)
|